Furthermore, as mentioned above, the frequency of a beam diffracted by an acoustic wave is shifted by the acoustic wave frequency times the diffraction order. So the multiple images made by diffracting a beam with multiple acoustic wave frequencies will each receive a different frequency shift. When the resulting images are used, e.g., to drive atomic transitions, the various diffraction orders corresponding to the different acoustic wave frequencies will be detuned from the transition by different amounts. In some types of quantum gates, this relatively small frequency shift does not matter (e.g. \({\sf R}_z\)  gates executed using differential Stark shifts on the qubit states [1]}, Raman gates with several GHz detuning [2]}, or gates using sub-picosecond laser pulses [3]}). Other quantum gates using resonant transitions might be affected by this detuning and will require additional addressing constraints or compensation strategies. For example, when driving two-photon transitions (each wavelength with its own scanner), then frequency shifts can be effectively compensated by having the frequency of the first and second photons of the transition being shifted by equal magnitudes but opposite signs [4]}. Despite such limitations, the multi-tone operation is particularly useful for situations when identical operations need to be performed in several sub-regions over the array. Such situations arise during initialization and syndrome measurement in logical qubits. Using multi-tone operation of AOD C, such operations can be performed in parallel, greatly saving operation time.
